相关论文: Free crossed resolutions for graph products of gro…
Let $G$ be a group which admits the structure of an iterated semidirect product of finitely generated free groups. We construct a finite, free resolution of the integers over the group ring of $G$. This resolution is used to define…
The C*-algebra of a skew-product topological graph is a crossed product of the C*-algebra of the base topological graph by a coaction.
The purpose of this note is to observe that a homomorphism of discrete groups $f:\Gamma\to G$ arises as the induced map $\pi_0(\mathfrak{M})\to \pi_0(\mathfrak{X})$ on path components of some closed normal inclusion of topological groups…
The recently introduced A-homotopy groups for graphs are investigated. The main concern of the present article is the construction of an infinite cell complex, the homotopy groups of which are isomorphic to the A-homotopy groups of the…
There has been significant research dedicated towards computing the crossing numbers of families of graphs resulting from the Cartesian products of small graphs with arbitrarily large paths, cycles and stars. For graphs with four or fewer…
We define and provide some basic analysis of various types of crossed products by semimultiplicative sets, and then prove a $KK$-theoretical descent homomorphisms for semimultiplicative sets in accord with the descent homomorphism for…
In this paper, we describe a regular representation given by Cayley theorem for 2-crossed modules of groups and their associated Gray 3-group groupoids with a single 0-cell and equivalently cat2-groups.
We give a survey on results regarding self-similar and automaton presentations of free groups and semigroups and related products. Furthermore, we discuss open problems and results with respect to algebraic decision problems in this area.
We classify $\mathcal{R}$- and $\mathcal{L}$-cross-sections of partial wreath product of inverse semigroups. As a corollary, we get the description of $\mathcal{R}$- and $\mathcal{L}$-cross-sections of the semigroupof partial automorphisms…
It is shown that quantum Euclidean groups $E_q(2)$, $E_\kappa(2)$ and $E_\kappa(3)$ have the structure of generalised crossed products.
The theory of representations of a crossed module is a direct generalization of the theory of representations of groups. For a finite group G, the Drinfeld quantum double of the group G is a Hopf algebra that represents a special case of…
Motivated by computational efficiency in algebraic automata theory here we define the cascade product of permutation groups as an external product, as a generic extension. It is the most general hierarchical product that uses arbitrary…
We study the problem of computing the homology of the configuration spaces of a finite cell complex $X$. We proceed by viewing $X$, together with its subdivisions, as a subdivisional space--a kind of diagram object in a category of cell…
We develop a unified framework based on topological crossed modules for various lifting obstructions for $\Gamma$-kernels. It allows us to identify actions, cocycle actions and $\Gamma$-kernels up to their natural equivalence relations with…
In a previous paper [1] [MR4101040], we initiated a systematic study of semihypergroups and had a thorough discussion about some important analytic and algebraic objects associated to this class of objects. In this paper, we investigate…
In this paper we study free actions of groups on separated graphs and their \cstar{}algebras, generalizing previous results involving ordinary (directed) graphs. We prove a version of the Gross-Tucker Theorem for separated graphs yielding a…
We provide explicit and unified formulas for the cocycles of all degrees on the normalized bar resolutions of finite abelian groups. This is achieved by constructing a chain map from the normalized bar resolution to a Koszul-like resolution…
This is the first out of two papers on independent resolutions for totally disconnected dynamical systems. In the present paper, we discuss independent resolutions from an algebraic point of view. We also present applications to group…
For any cssc-crossed module a category is constructed, equipped with a structure and proved that this is a coherent categorical group. Together with a result of the previous paper, where to any categorical group the cssc-crossed module is…
We show how the framework of crossed simplicial groups may be used to provide a classification of topological field theories on open cobordism categories defined by reductions of the structure group to a planar Lie group. Such theories are…